a) The analysis of measured wind data results in a mean wind speed of v = 8 m/s and a variance
of ĻĀ² = 2.89 mĀ²/sĀ². What is the corresponding turbulence intensity I?
b) Another measurement, taken at a location with roughness length zo = 0.03 m at 10 m height,
results in a mean wind speed of v = 10 m/s. Using the logarithmic wind profile calculate the
mean wind speed at 100 m.
c) For a certain location the shape parameter k of the Weibull distribution of the mean wind
speeds is known to be k = 2.0 and the long-time average wind speed is (v) = 7 m/s. Determine
the corresponding scale parameter A of the Weibull distribution by using the approximate
formula given in the lecture.
d) By which factor does the power in the wind change if the wind speed increases from 5 m/s to
10 m/s?
e) How does the wind speed behave depending on the height at an offshore location and at an
onshore location, respectively? To answer this question, draw a qualitative sketch of a diagram
and denote both curves.
f) Consider an offshore location (a = 0.14) and an onshore location (a = 0.2). At both locations a
wind turbine is planned which should see a mean wind speed of hub = 8 m/s at hub height. At
both locations the measured mean wind speed at 100 m is 100 = 9.0 m/s. Based on the power
law dependence of wind speed on height above ground (Hellmann formula):
$$v(z_2) = v(z_1) \left(\frac{z_2}{z_1}\right)^\alpha$$.
Which hub heights have to be chosen at the offshore and at the onshore location, respectively?
g) In the lecture as well as in the exercises you have learned a formula to calculate the power,
which a wind turbine can extract from an air mass flow. Using this formula complete the
following table. Write down your approach to the solution. Take care of the units! (4 Points)
Diameter D
[m]
Wind speed v
[km/h]
Air density p
[kg/mĀ³]
Power coefficient Cp
[-]
Power P
[MW]
1.
120
36.0
1.225
0.490
II.
34.2
1.225
0.480
2.4
h) Based on Betz's theory, is it possible to realize a wind turbine (rotor diameter 90 m) with rated
power 3,0 MW at rated wind speed 10 m/s and an air density of 1.225 kg/mĀ³? Give a reason for
your answer.
i) Determine the number of wind turbines needed to generate 30 MWh of electricity per day if
each turbine is 40% efficient, has a rotor radius of 40 m, and is powered by a wind stream with a
constant velocity of 18 km/h. Assume an air density of 1.225 kg/mĀ³ and that the wind blows
for only 16 hours per day.